I think men should care about the relationship they have built with a child and not reject a child, in any way, with whom they have developed that bond.
His ex wife's actions are despicable, clearly.
My husband is bringing up a child that is not 'his' biologically, although he is of course fully aware of the fact. If I were a morally bankrupt individual and just didn't tell him it wasn't 'his' - it would still be 'his', they would still be father and child. It's about children, not biology.